A random variable X follows the exponential distribution if it has the following probability density function (PDF): f(X) = (1/)e -X/ for X > 0

A random variable X follows the exponential distribution if it has the following probability density function (PDF):

f(X) = (1/θ)e^-X/θ           for X > 0

= 0                               elsewhere

where θ > 0 is the parameter of the distribution. Using the ML method, show that the ML estimator of θ is θ̂ = ΣX_i /n, where n is the sample size. That is, show that the ML estimator of θ is the sample mean X̅.